arXiv subjects

S. Sridhar

Publications and source records attributed to S. Sridhar.

At least 37 records · Page 2Linked to original sources

arXiv2014

Large-scale dynamo action due to $α$ fluctuations in a linear shear flow

We present a model of large-scale dynamo action in a shear flow that has stochastic, zero-mean fluctuations of the $α$ parameter. This is based on a minimal extension of the Kraichnan-Moffatt model, to include a background linear shear and Galilean-invariant $α$-statistics. Using the first order smoothing approximation we derive a linear integro-differential equation for the large-scale magnetic field, which is non perturbative in the shearing rate $S\,$, and the $α$-correlation time $τ_α\,$. The white-noise case, $τ_α= 0\,$, is solved exactly, and it is concluded that the necessary condition for dynamo action is identical to the Kraichnan-Moffatt model without shear; this is because white-noise does not allow for memory effects, whereas shear needs time to act. To explore memory effects we reduce the integro-differential equation to a partial differential equation, valid for slowly varying fields when $τ_α$ is small but non zero. Seeking exponential modal solutions, we solve the modal dispersion relation and obtain an explicit expression for the growth rate as a function of the six independent parameters of the problem. A non zero $τ_α$ gives rise to new physical scales, and dynamo action is completely different from the white-noise case; e.g. even weak $α$ fluctuations can give rise to a dynamo. We argue that, at any wavenumber, both Moffatt drift and Shear always contribute to increasing the growth rate. Two examples are presented: (a) a Moffatt drift dynamo in the absence of shear; (b) a Shear dynamo in the absence of Moffatt drift.

astro-ph.GA↗

arXiv2012

Light beams with general direction and polarization: global description and geometric phase

We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S^2 of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S^2 X C^2, the Cartesian product of a sphere and a two dimensional complex vector space. A Hopf map (i.e mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S^2 X S^2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP^2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S^2 X S^2. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.

physics.optics↗

arXiv2012

Estimation of Effort in Software Cost Analysis for Heterogenous Dataset using Fuzzy Analogy

One of the significant objectives of software engineering community is to use effective and useful models for precise calculation of effort in software cost estimation. The existing techniques cannot handle the dataset having categorical variables efficiently including the commonly used analogy method. Also, the project attributes of cost estimation are measured in terms of linguistic values whose imprecision leads to confusion and ambiguity while explaining the process. There are no definite set of models which can efficiently handle the dataset having categorical variables and endure the major hindrances such as imprecision and uncertainty without taking the classical intervals and numeric value approaches. In this paper, a new approach based on fuzzy logic, linguistic quantifiers and analogy based reasoning is proposed to enhance the performance of the effort estimation in software projects dealing with numerical and categorical data. The performance of this proposed method illustrates that there is a realistic validation of the results while using historical heterogeneous dataset. The results were analyzed using the Mean Magnitude Relative Error (MMRE) and indicates that the proposed method can produce more explicable results than the methods which are in vogue.

cs.SE↗

arXiv2012

Optimization of fuzzy analogy in software cost estimation using linguistic variables

One of the most important objectives of software engineering community has been the increase of useful models that beneficially explain the development of life cycle and precisely calculate the effort of software cost estimation. In analogy concept, there is deficiency in handling the datasets containing categorical variables though there are innumerable methods to estimate the cost. Due to the nature of software engineering domain, generally project attributes are often measured in terms of linguistic values such as very low, low, high and very high. The imprecise nature of such value represents the uncertainty and vagueness in their elucidation. However, there is no efficient method that can directly deal with the categorical variables and tolerate such imprecision and uncertainty without taking the classical intervals and numeric value approaches. In this paper, a new approach for optimization based on fuzzy logic, linguistic quantifiers and analogy based reasoning is proposed to improve the performance of the effort in software project when they are described in either numerical or categorical data. The performance of this proposed method exemplifies a pragmatic validation based on the historical NASA dataset. The results were analyzed using the prediction criterion and indicates that the proposed method can produce more explainable results than other machine learning methods.

cs.SE↗

arXiv2012

Mean field dynamo action in renovating shearing flows

We study mean field dynamo action in renovating flows with finite and non zero correlation time ($τ$) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and non helical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly non helical, then such mean field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval $τ$. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the $α^2 Ω$ dynamo, in the small $τ$ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.

astro-ph.GA↗

arXiv2012

Counter-rotating stellar discs around a massive black hole: self-consistent, time-dependent dynamics

We formulate the collisionless Boltzmann equation (CBE) for dense star clusters that lie within the radius of influence of a massive black hole in galactic nuclei. Our approach to these nearly Keplerian systems follows that of Sridhar and Touma (1999): Delaunay canonical variables are used to describe stellar orbits and we average over the fast Keplerian orbital phases. The stellar distribution function (DF) evolves on the longer time scale of precessional motions, whose dynamics is governed by a Hamiltonian, given by the orbit-averaged self-gravitational potential of the cluster. We specialize to razor-thin, planar discs and consider two counter-rotating ("$\pm$") populations of stars. To describe discs of small eccentricities, we expand the $\pm$ Hamiltonian to fourth order in the eccentricities, with coefficients that depend self-consistently on the $\pm$ DFs. We construct approximate $\pm$ dynamical invariants and use Jeans' theorem to construct time-dependent $\pm$ DFs, which are completely described by their centroid coordinates and shape matrices. When the centroid eccentricities are larger than the dispersion in eccentricities, the $\pm$ centroids obey a set of 4 autonomous ordinary differential equations. We show that these can be cast as a two-degree of freedom Hamiltonian system which is nonlinear, yet integrable. We study the linear instability of initially circular discs and derive a criterion for the counter-rotating instability. We then explore the rich nonlinear dynamics of counter-rotating discs, with focus on the variety of steadily precessing eccentric configurations that are allowed. The stability and properties of these configurations are studied as functions of parameters such as the disc mass ratios and angular momentum.

astro-ph.GA↗

arXiv2012

Unstable $m=1$ modes of counter-rotating Keplerian discs

We study the linear $m=1$ counter-rotating instability in a two-component, nearly Keplerian disc. Our goal is to understand these \emph{slow} modes in discs orbiting massive black holes in galactic nuclei. They are of interest not only because they are of large spatial scale--and can hence dominate observations--but also because they can be growing modes that are readily excited by accretion events. Self-gravity being nonlocal, the eigenvalue problem results in a pair of coupled integral equations, which we derive for a two-component softened gravity disc. We solve this integral eigenvalue problem numerically for various values of mass fraction in the counter-rotating component. The eigenvalues are in general complex, being real only in the absence of the counter-rotating component, or imaginary when both components have identical surface density profiles. Our main results are as follows: (i) the pattern speed appears to be non negative, with the growth (or damping) rate being larger for larger values of the pattern speed; (ii) for a given value of the pattern speed, the growth (or damping) rate increases as the mass in the counter-rotating component increases; (iii) the number of nodes of the eigenfunctions decreases with increasing pattern speed and growth rate. Observations of lopsided brightness distributions would then be dominated by modes with the least number of nodes, which also possess the largest pattern speeds and growth rates.

astro-ph.GA↗

arXiv2011

A Classical Fuzzy Approach for Software Effort Estimation on Machine Learning Technique

Software Cost Estimation with resounding reliability,productivity and development effort is a challenging and onerous task. This has incited the software community to give much needed thrust and delve into extensive research in software effort estimation for evolving sophisticated methods. Estimation by analogy is one of the expedient techniques in software effort estimation field. However, the methodology utilized for the estimation of software effort by analogy is not able to handle the categorical data in an explicit and precise manner. A new approach has been developed in this paper to estimate software effort for projects represented by categorical or numerical data using reasoning by analogy and fuzzy approach. The existing historical data sets, analyzed with fuzzy logic, produce accurate results in comparison to the data set analyzed with the earlier methodologies.

cs.SE↗

arXiv2011

Critical role of pinning defects in scroll-wave breakup in active media

The breakup of rotating scroll waves in three-dimensional excitable media has been linked to important biological processes. The known mechanisms for this transition almost exclusively involve the dynamics of the scroll filament, i.e., the line connecting the phase singularities. In this paper, we describe a novel defect-induced route to breakup of a scroll wave pinned by an inexcitable obstacle partially extending through the bulk of the medium. The wave is helically wound around the defect inducing sudden changes in velocity components of the wavefront at the obstacle boundary. This results in breakup far from the filament, eventually giving rise to spatiotemporal chaos. Our results suggest a potentially critical role of pinning obstacles in the onset of life-threatening disturbances of cardiac activity.

nlin.PS↗

arXiv2011

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in Sridhar & Singh (JFM, 664, 265, 2010), and present a theory of the \emph{shear dynamo problem} for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients, $α_{il}$ and $η_{iml}$, are derived. We prove that, when the velocity field is non helical, the transport coefficient $α_{il}$ vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean--invariant forcing statistics. We consider forcing statistics that is non helical, isotropic and delta-correlated-in-time, and specialize to the case when the mean-field is a function only of the spatial coordinate $X_3$ and time $τ\,$; this reduction is necessary for comparison with the numerical experiments of Brandenburg, R{ä}dler, Rheinhardt & Käpylä (ApJ, 676, 740, 2008). Explicit expressions are derived for all four components of the magnetic diffusivity tensor, $η_{ij}(τ)\,$. These are used to prove that the shear-current effect cannot be responsible for dynamo action at small $\re$ and $\rem$, but for all values of the shear parameter.

astro-ph.GA↗

arXiv2011

Robust method to determine the resolution of a superlens by analyzing the near-field image of a two-slit object

In the last decade, metamaterials-based superlenses, with a resolution below Abbe's diffraction limit, have emerged. To obtain a rough estimate of the resolution of such superlenses, imaging of two subwavelength slits, separated by a subwavelength gap \textit{d} is typically performed. The resolution $Δ$ of the lens corresponds to the minimum possible gap $d_{min}$ for which a distinct image of the two slits can be resolved ($Δ\sim d_{min}$). In this letter, we present a more quantitative estimate of the resolution of manufactured lenses by fitting analytical near-field image profiles, obtained from imaging a two-slit object with a theoretical negative-index lens of known resolution, to experimental data. We conclude the discussion by applying our analytical method to 3 case examples of superlensing from the literature. As shown, this method is particularly attractive for rapidly assessing the performance of fabricated superresolution lenses.

physics.optics↗

arXiv2010

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow, in the low conductivity limit. Our treatment is nonperturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Rm) but could have arbitrary fluid Reynolds number. The magnetic fluctuations are determined to lowest order in Rm by explicit calculation of the resistive Green's function for the linear shear flow. The mean electromotive force is calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the C and D terms, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the spacetime integrals. The contribution of the D terms is such that the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves. Therefore, to lowest order in Rm but to all orders in the shear strength, the D terms cannot give rise to a shear-current assisted dynamo effect. Casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors. The integral kernels are expressed in terms of the velocity spectrum tensor, which is the fundamental quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field.

astro-ph.GA↗

arXiv2010

Wave-train induced unpinning of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

physics.bio-ph↗

arXiv2010

Response to sub-threshold stimulus is enhanced by spatially heterogeneous activity

Sub-threshold stimuli cannot initiate excitations in active media, but surprisingly as we show in this paper, they can alter the time-evolution of spatially heterogeneous activity by modifying the recovery dynamics. This results in significant reduction of waveback velocity which may lead to spatial coherence, terminating all activity in the medium including spatiotemporal chaos. We analytically derive model-independent conditions for which such behavior can be observed.

nlin.CD↗

arXiv2010

Slow light, open cavity formation, and large longitudinal electric field on slab waveguide made of indefinite permittivity materials

The optical properties of slab waveguides made of indefinite permittivity ($\vep$) materials (IEM) are considered. In this medium the transverse permittivity is negative while the longitudinal permittivity is positive. At any given frequency the waveguide supports an infinite number of transverse magnetic (TM) eigenmodes. For a slab waveguide with a fixed thickness, at most only one TM mode is forward-wave. The rest of them are backward waves which can have very large phase index. At a critical thickness, the waveguide supports degenerate forward- and backward-wave modes with zero group velocity. Above the critical thickness, the waveguide supports complex-conjugate decay modes instead of propagating modes. The presence of loss in IEMs will lift the degeneracy, resulting in modes with finite group velocity. Feasible realization is proposed. The performance of IEM waveguide is analyzed and possible applications are discussed which are supported by numerical calculations. These slab waveguides can be used to make optical delay lines in optical buffers to slow down and trap light, to form open cavities, to generate strong longitudinal electric fields, and as phase shifters in optical integrated circuits.

physics.optics↗

arXiv2010

Nonperturbative quasilinear approach to the shear dynamo problem

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow. Our treatment is quasilinear and equivalent to the standard `first order smoothing approximation'. However it is non perturbative in the shear strength. We first derive an integro-differential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We show that, for non helical turbulence, the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves; this is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence, to all orders in the shear parameter, there is no shear-current type effect for non helical turbulence in a linear shear flow, in quasilinear theory in the limit of zero resistivity. We then develop a systematic approximation of the integro-differential equation for the case when the mean magnetic field varies slowly compared to the turbulence correlation time. For non-helical turbulence, the resulting partial differential equations can again be solved by making a shearing coordinate transformation in Fourier space. The resulting solutions are in the form of shearing waves, labeled by the wavenumber in the sheared coordinates. These shearing waves can grow at early and intermediate times but are expected to decay in the long time limit.

astro-ph.GA↗

arXiv2009

Slow pressure modes in thin accretion discs

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber $m=1$. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate--through WKB analysis and numerical solution of the eigenvalue problem--that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schrödinger-like equation. Analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power law discs, albeit for physically uninteresting values of the power law index $β$ and barotropic index $γ$.

astro-ph.GA↗

arXiv2009

Magnetohydrodynamic turbulence in a strongly magnetised plasma

I present a review of incompressible magnetohydrodynamic (MHD) turbulence in a strongly magnetised plasma. The approach is phenomenological even where a more rigorous theory is available, so that a reader armed with paper, pencil and some determination may be able to work through most of the physics. The focus is on the inertial-range spectra for very large (fluid and magnetic) Reynolds numbers. These theories of the inertial-range are built on two important facts: (i) Kraichnan's insight that the turbulent cascades are a result of nonlinear interactions between oppositely directed wavepackets of Elsasser fields; (ii) these oppositely directed wavepackets do not exchange energy, but contribute only to changing each other's spatial structures. I begin with a description and critique of the Iroshnikov-Kraichnan theory, and explore the fundamental departures necessitated by the anisotropic nature of the turbulence. Derivations of the inertial-range spectra of four regimes of MHD turbulence -- the balanced weak, balanced strong, imbalanced weak and the imbalanced strong cascades -- are then presented. The need for studying the spectra of imbalanced turbulence when the waves on the outer scale have a short correlation time is briefly discussed.

astro-ph.GA↗